Dog

Check with your vet to be sure that all of your pets are healthy before introducing the new dog to your family.

Dog to dog:
Bringing home a new pup always requires a period of transition and adjustment for other pets in the household – even very friendly animals must figure out how to share food, territory and your affection with the new guy. Gradual introductions are important; the new pup should be kept separate from the other pets at first, confined to a ‘neutral’ room like the laundry room or a bathroom (not anywhere that is considered highly desirable by the other pets, such as the kitchen or your bedroom) with a few toys, blanket and water. Spend some quality time alone with the new pup, then bring him outside on a leash and introduce him calmly to the other animals.

If the household animals are calm and ignore each other, or act friendly, you can feed them within sight of the new pet. Feeding and petting the dogs in each other's presence teaches them that good things happen when they are together and calm. If any of them reacts violently, banish him to a neutral zone immediately and try again when he’s calm. If he again reacts violently, banish him for the rest of the day and try again in the evening or the next morning. Watch for subtle threatening behaviors in every interaction between the old and new animals: raised hackles, staring, snarling, stalking, side-by-side posturing with growling or lip lifting are a few. If the new pup seems to be losing the contest, is scared or is becoming too aggressive, separate the dogs. Reward even the tiniest example of good behavior with small food treats, lavish praise and plenty of petting. Have patience, let all the pets know that bad behavior won’t be tolerated, and sooner or later they’ll work it out amongst themselves.

Dog to Cat:
Introducing a new dog to a cat is not always a slam dunk. To some degree its success depends on the characteristics of your dog’s breed – some dog breeds are friendly and welcoming by nature – and others were bred generations ago specifically to hunt down small furry animals. Like cats. Assessing which sort of dog you’ve got, and making sure he’ll obey your wishes matters very much to your existing kitty’s safety and well-being.If you yourself are not the Alpha dog in your household - if your dog hasn’t graduated from obedience training with you - then Fido likely won’t respect your wishes, and no kitty would be safe in an unsupervised situation under those circumstances.

Realize this: You can’t control the cat. You can only work to control the dog. When doggy does something right, lavish him with praise. But if the dog makes a mistake, NEVER punish! It’ll just make the cat-dog relationship that much more problematic. Just try again - and have patience, it could take some time to get it right.
Begin the introduction with these steps:

Keep your new dog isolated from your cat, in his own safe and secure room.

Swap scents; using an old blanket or towel, give the item to your new dog. Let him play on it, sleep on it, eat on it. Rub him with this blanket and then leave it in his room for 24 hours.

Remove the blanket and present it to your kitty. Rub him all over with it, let him roll on it, sniff it, sleep on it for 24 hours, then switch and do the same thing again. This blends their scents, helping to make them more at ease with each other.

Use a soft plush dog toy, give it to the dog first, let him play with it, slobber on it and then toss the toy into kitty’s space. Just leave that toy there for a couple of days.

Feed your resident pets and the newcomer on each side of the door to the dog’s room. This will help all of them to associate something enjoyable (eating!) with each other's smells. Don't put the food next to the door if the animals are too upset by each other's presence to eat; instead gradually move the dishes closer to the door until your pets can eat calmly, directly on either side of the door. At the next meal, use two doorstops to prop open the door an inch or so to allow the animals to see each other, and repeat the whole process.

Under strict supervision (and with one hand firmly restraining Fido by the collar, even if he hasn’t seemed aggressive up til now) it’s time to open the door and begin formal nose to nose introductions.

Remember that a dog can kill a cat very easily, even if he’s only playing. All it takes is one shake and the cat's neck can break. Even a friendly dog will usually want to chase and play with cats, and cats will quickly become afraid and defensive. Once again, cats and dogs should never be unsupervised until you’re sure neither will attack – and only if you’re confident that you can control Fido through obedience commands if their interaction gets out of control.

Kittens And Puppies
Because they're so much smaller, kittens are in more danger of being injured or killed by a young, energetic or predatory puppy. A kitten will need to be kept separate from an energetic or predatory dog until fully-grown, and even then kitty should never be left alone with the dog. Usually, a well-socialized cat will be able to keep a puppy in its place, but some cats don't have the confidence to do this. If you have an especially shy cat, you might need to keep him separated from your puppy until Fido graduates from thorough obedience training, has been well-socialized to kitty by watching you interact with the cat for several months, and has matured enough to practice self-control around the cat.